Question

2+4+6+...+200
2+5+8+...+242 cu cat este egal

Answer 1

2+4+6+...+200=
Aplicam Suma lui Gauss$= \frac{n(n+1)}{2} .$
$= \frac{200(200+1)}{2} = \frac{200*201}{2} = \frac{40200}{2} \boxed{=20100.}$

2+5+8+...+242=
$= \frac{n(n+1)}{2}= \frac{242(242+1)}{2}= \frac{242*243}{2} = \frac{58806}{2} \boxed{=29403.}$

Answer 2

$\displaystyle a).2+4+6+...+200=2(1+2+3+...+100)=2 \times \frac{100(100+1)}{2} = \\ \\ =2 \times \frac{100 \times 101}{2} =\not 2 \times \frac{10100}{\not 2} =10100$

$\displaystyle b).2+5+8+...+242 \\ \\ 242=2+(n-1) \times 3 \\ \\ 242=2+3n-3 \\ \\ 3n=242-2+3 \\ \\ 3n=243 \\ \\ n= \frac{243}{3} \\ \\ n=81$

$\displaystyle S_{81}= \frac{4+80 \times 3}{2} \times 81 \\ \\ S_{81}= \frac{4+240}{2} \times 81 \\ \\ S_{81}= \frac{244}{2} \times 81 \\ \\ S_{81}= 122 \times 81 \\ \\ S_{81}=9882$